Problem: Simplify the following expression: $r = \dfrac{9x}{5} + \dfrac{x}{9}$
Solution: In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $5$ and $9$ $\lcm(5, 9) = 45$ $ r = \dfrac{9}{9} \cdot \dfrac{9x}{5} + \dfrac{5}{5} \cdot \dfrac{x}{9} $ $r = \dfrac{81x}{45} + \dfrac{5x}{45}$ $r = \dfrac{81x +5x}{45}$ $r = \dfrac{86x}{45}$